Spec Ops: The Line is probably the first example that comes to mind.
They get a bad rap because of the sometimes fascist leaning fanbase, but paradox grand strategy games do let you play whatever side you want. Everytime I tried Hearts of Iron (admittedly my least favourite paradox game), I played as the USSR.
Some of the Metal Gear games, though that's still "the good americans vs the corrupt government" which isn't really ideal either.
Yakuza 3 features CIA as one of the villain factions.
There a couple very specific eras of JRPGs that hold a very special place in my memory.
The Super Famicom era around games like Chrono Trigger is the peak for me though. I remember I got it as a gift totally by mistake, my parents had meant to buy another game but got possibly my favourite game of all time instead. I can still go back and play that game and it holds up just fine.
PS1 era Squaresoft was also pretty much a golden era for me, Xenogears was a pretty massive influence on some of my younger intellectual development.